科研之友
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摘要
In this paper, we shall study the initial-boundary value problem of a mathematical model describing the branching of capillary sprouts during angiogenesis in one dimensional space. Under homogeneous Neumann boundary conditions, we show the existence of a unique global classical solution with uniform-in-time bound for all suitably regular initial data. Moreover, we show that the unique solution will exponentially converge to a non-trivial constant steady state as time tends to infinity under some appropriate conditions on the parameters.
